Problem: Rewrite as a simplified fraction. ${3.7\overline{8} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 378.8888...\\ 10x &= 37.8888...\end{align*}}$ Subtracting the two equations, we have: ${90x = 341}$ ${x = \dfrac{341}{90}} \text{or} {3 \dfrac{71}{90}}$